First half goals from Calvert-Lewin and Macauley |Bonne saw the teams go in at half time level, with the U's being the better team in possession.
The second half started badly for the U's though, with Watson scoring early, only for Bonne to score another equaliser eight minutes from time.
The home side grabbed the win two minutes later, with sub Richards deflecting a shot in to make it 3-2.
Tony Humes made five changes to his starting line-up, bringing in Frankie Kent, Matt Briggs, Sammie Szmodics, Owen Garvan and Dion Sembie-Ferris.
And it was the young winger Sembie-Ferris who created the first chance in the game, having a low cross blocked for a corner.
A minute later, it was 1-0 to the hosts though, as Calvert-Lewin got on the end of a cross from the U’s right hand side.
Hoskins found himself in space as a through ball was played behind the U’s defence and a drilled cross was chested past Parish to give the Cobblers the lead.
The goal obviously gave the Northampton forward the confidence to try his luck again a minute later, this time finding Parish with a shot from twenty yards out.
The home side were looking to get men forward whenever they could but they were caught on the break on twenty minutes, with Matt Briggs the player to profit.
He burst forward and after beating a couple of players, rolled the ball to Harriott, who in turn found Moncur racing forward from midfield.
Moncur couldn’t find the space for a shot initially but manoeuvred the ball onto his right foot but found Clarke in the home goal with his curling effort.
Sembie-Ferris and Harriott were trying to get in behind the home defence on either flank and on the half hour, both managed just that.
On the half hour, Sembie-Ferris found Bonne on the near post but the young striker couldn’t get a shot away under pressure from his marker.
Bonne wasn’t to be denied for long though, and headed home at the far post to level the scores when Harriott put in a dangerous cross from the left.
The U’s were having to look for another equaliser only four minutes into the second half, as Watson scored the goal of the game.
Watson picked the ball up just inside his own half, drove forward and unleashed an unstoppable shot past Parish to put his side 2-1 up.
An instant reply looked on the cards but Briggs’ effort flew just over the crossbar a minute after the Watson goal.
The U’s began to control the game and were creating chances to get back into the game.
Szmodics headed wide, Moncur narrowly missed the target and Bonne put a volley over the bar from just outside the box.
On the hour, Drey Wright replaced Sembie-Ferris and the U’s continued to dominate possession and territory.
Parish did have to make a save from D’Ath on sixty five minutes but the play quickly returned to the other end, with Alex Wynter just failing to make contact with his header.
Bonne almost scored when he followed up Moncur’s shot but his effort rolled the wrong side of the upright.
He did manage to get his and the U’s second though, as her smartly finished an incisive move.
Szmodics, Moncur and Harriott were all involved and the latter’s final ball was perfect for Bonne to take a touch and calmly put his shot past Clarke to make it 2-2 with eight minutes to play.
It only took the home side a further two minutes to regain the lead, with sub Richards getting a fortunate deflection.
Harriott allowed his man to get goal side and from the cross, a shot hit Richards and flew past Parish to make it 3-2.
The hosts then comfortably saw out the remaining six minutes, and four of added time, to progress into the Second Round.
With the weekend’s game against Sheffield United postponed because of the Blades’ international call ups, the U’s will have to wait eleven days before they take to the field again.